Quadratic Ideals, Indefinite Quadratic Forms and Some Specific Diophantine Equations


TEKCAN A. , Kutlu S.

BOLETIM SOCIEDADE PARANAENSE DE MATEMATICA, vol.36, no.3, pp.173-192, 2018 (Journal Indexed in ESCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 36 Issue: 3
  • Publication Date: 2018
  • Doi Number: 10.5269/bspm.v36i3.30799
  • Title of Journal : BOLETIM SOCIEDADE PARANAENSE DE MATEMATICA
  • Page Numbers: pp.173-192

Abstract

Let k >= 1 be an integer and let P = k + 2, Q = k and D = k(2) + 4. In this paper, we derived some algebraic properties of quadratic ideals I-gamma and indefinite quadratic forms F-gamma for quadratic irrationals gamma, and then we determine the set of all integer solutions of the Diophantine equation F-gamma(+/- k) (x, y) = +/- Q.